STOCHASTIC BURGERS EQUATION WITH LÉVY SPACE-TIME WHITE NOISE

Abstract:

The purpose of this paper is to investigate the Cauchy problem for the following stochastic Burgers equation

with suitable initial condition (for all (t,x)∈[0,∞)×ℝ), where F_t,x is a Lévy space-time white noise. The problem is interpreted as a stochastic integral equation of jump type involving the heat kernel. We obtain existence of a unique local solution in the L² sense and show that it gives rise to a (local) stochastic flow (in time).